Related papers: Finding the Kraus decomposition from a master equa…
We present a quantum algorithm for simulating a family of Markovian master equations that can be realized through a probabilistic application of unitary channels and state preparation. Our approach employs a second-order product formula for…
It is shown how the phase-damping master equation, either in Markovian and nonMarkovian regimes, can be obtained as an averaged random unitary evolution. This, apart from offering a common mathematical setup for both regimes, enables us to…
We describe temporally correlated noise processes that influence the idle evolution of a superconducting transmon qubit. To model the composite qubit-environment system we use quantum circuit theory, and we show how a circuit Hamiltonian…
We investigate some classical evolution model in the discrete 2+1 space-time. A map, giving an one-step time evolution, may be derived as the compatibility condition for some systems of linear equations for a set of auxiliary linear…
Data of the numerical solution of the time-dependent Schr\"odinger equation of a system containing one spin-1/2 particle interacting with a bath of up to 32 spin-1/2 particles is used to construct a Markovian quantum master equation…
The exact solution of the Lindblad equation with a quadratic Hamiltonian and linear coupling operators was derived within the chord representation, that is, for the Fourier transform of the Wigner function, also known as the characteristic…
Using the Carleman linearization technique the continuous iteration of a mapping is studied. Based on the detailed analysis of the Carleman embedding matrix the precise mathematical meaning is given to such notion. The ordinary differential…
Dynamics of an open $N$-state quantum system is typically modeled with a Markovian master equation describing the evolution of the system's density operator. By using generators of $SU(N)$ group as a basis, the density operator can be…
Quantum systems coupled to environments exhibit intricate dynamics. The master equation gives a Markov approximation of the dynamics, allowing for analytic and numerical treatments. It is ubiquitous in theoretical and applied quantum…
The Hilbert space formalism of quantum theory manifests a map between bipartite states and time evolutions, known as Jamiolkowski isomorphism. We extend this map in a physical setting to prove the equality of spatial correlations in…
In open quantum systems, phenomenological master equations with unknown parameters are often introduced. Here we propose a time-independent procedure based on quantum tomography to reconstruct the potentially unknown parameters of a wide…
The Lindblad equation is an evolution equation for the density matrix in quantum theory. It is the general linear, Markovian, form which ensures that the density matrix is hermitian, trace 1, positive and completely positive. Some…
A new theoretical framework, based on the quantum field theory of open systems applied to neutrinos, has been developed. This framework aims to describe the neutrino evolution in external environment, taking into account the effect of…
Here we present a Lindblad master equation that approximates the Redfield equation, a well known master equation derived from first principles, without significantly compromising the range of applicability of the Redfield equation. Instead…
We introduce a new regularization of the Redfield equation based on a replacement of the Kossakowski matrix with its closest positive semidefinite neighbor. Unlike most of the existing approaches, this procedure is capable of retaining the…
The theoretical description of the interplay between coherent evolution and chemical exchange, originally developed for magnetic resonance and later applied to other spectroscopic regimes, was derived under incorrect statistical…
We present an alternative (constructive) proof of the statement that for every completely positive, trace-preserving map $\Phi$ there exists an auxiliary Hilbert space $\mathcal K$ in a pure state $|\psi\rangle\langle\psi|$ as well as a…
We provide a rigorous construction of Markovian master equations for a wide class of quantum systems that encompass quadratic models of finite size, linearly coupled to an environment modeled by a set of independent thermal baths. Our…
We study the spatially homogeneous time dependent solutions and their bifurcations of the Gray-Scott model. We find the global map of bifurcations by a combination of rigorous verification of the existence of Takens Bogdanov and a Bautin…
It is known that the dynamical evolution of a system, from an initial tensor product state of system and environment, to any two later times, t1,t2 (t2>t1), are both completely positive (CP) but in the intermediate times between t1 and t2…